Question

Sky invests $90,000 today and receives a future value 8 years from now of $120,000. Interest is compounded twice per year. Her stated annual interest rate is _____ for this twice-a-year compounded investment.

Answer 1

Answer:

Annual interest rate= 3.63%

Explanation:

The rate of return earned on the investment can be worked out using the Future value of a lump sum formula.

The future value of a lump sum is the amount lump would amount to if interest is earned and compounded at a certain interest rate.

The formula is

FV = PV × (1+r)^(n)  

PV = Present Value- 90,000

FV - Future Value, - 120,000

n- number of period- 8× 2 = 16 (note interest is compounded twice a year)

r- interest rate per period - ?

120,000 = 90,000× (1+r)^16

1+r)^16= 120.000/90,000= 1.333

(1+r)^16= 1.333

1+r= 1.333^(1/16)

r =1.333^(1/16) -1  = 0.01812

r =0.01812× 100= 1.812%

Bi-annual interest rate = 1.812%

Annual interest rate = Bi-annual rate × 2

Annual interest rate = 1.812% × 2 =3.63%

Annual interest rate= 3.63%